A (1, -3)
B (2, -4)
A' (4, -12)
B' (8, -16)
Determine the scale factor used in the dilation of line segment AB, centered at the origin.
(1 point)
0 4
1/4
0-4
2
The scale factor is 4. This can be determined by dividing the length of A'B' by the length of AB.
Length of AB = sqrt((2-1)^2 + (-4-(-3))^2) = sqrt(1 + 1) = sqrt(2)
Length of A'B' = sqrt((8-4)^2 + (-16-(-12))^2) = sqrt(16 + 16) = sqrt(32)
Scale factor = Length of A'B' / Length of AB = 4 / sqrt(2) = 4sqrt(2) / 2 = sqrt(2) = 4